Do character controllers work with dynamic gravity?

Hello!

I'm creating a small first-person puzzle platformer to learn Unity. I want the player character to be able to walk up ramps, but not be able to walk up steep inclines. So, naturally, I was going to use a character controller to accomplish this.

But my game is going to have dynamic gravity. One minute you're standing on the floor; the next you're on the wall. At one type, the player is allowed to traverse inclines between -30 and 30; the next minute they're allowed to walk on anything between 60 and 120. Can a character controller be implemented/used in this way? Are there any resources or examples that teach me how to accomplish this?

Thanks.